1. Field of the Invention
The invention relates to a multiple speed transmission system, and more particularly to a transmission system for driving the shaft of a winding or unwinding apparatus to keep the surface speed and web tension of a roll being wound or unwound substantially constant while the roll diameter changes.
2. Description of the Prior Art
Various operations in the manufacture and processing of paper, film, foil and other flexible sheet materials in web form involve the winding, unwinding and rewinding of rolls of the web material. The maintenance of constant operating conditions requires that the surface speed and tension of the web be kept constant during unwinding winding and rewinding. To maintain constant surface speed and web tension as the diameter of a roll increases the drive speed of the core on which the material is being wound must be steadily reduced. The mass of the roll increases. Accordingly the drive to the core of a winder or rewinder requires some means for increasing torque output and reducing speed to maintain the tension in the material at a constant level while also keeping the surface speed constant.
These purposes can, or course, be achieved by use of a drive motor operating at varying speeds and producing varying torque. The motor-generator of "MG" drive can be effectively used for winding of web material. In such an MG drive an AC motor is used to drive a DC generator which in turn provides current to drive a variable torque, variable speed DC motor on the winder drive. Such systems are commercially available but very expensive.
In many cases it is more desirable to use a drive motor operating at constant speed. A constant speed motor can be used to drive a winding apparatus through a slip clutch or eddy current clutch, in which case the difference between the motor speed and the decreasing speed of rotation required for constant surface speed of material being wound must be speed lost in the clutch. Thus the slippage in a slip clutch used in such an arrangement would constantly increase as the roll goes from its small starting diameter to its final large diameter. The motion lost in the clutch can be considered as power absorbed and dissipated by the clutch. As used in this application, the term "slip clutch" refers to a clutch which permits slippage constantly during drive, not just upon engagement or under overload conditions.
The following example illustrates the great inefficiency of using a constant speed motor and a slip clutch to drive a rewind apparatus. In this example, paper, after processing, is wound on a core having a diameter of 31/2 inches until a roll having a diameter of 60 inches has been wound. The surface speed of the paper web is maintained at 1000 feet per minute and the tension in the web is kept at 250 pounds to assure the formation of a uniform roll.
The speed of rotation of the drive shaft of the rewind device varies directly with the surface speed and inversely with the diameter of the roll. Since the surface speed is kept constant, the reduction in speed from beginning at a diameter of 31/2 inches and ending at a full roll diameter of 60 inches entails a speed reduction ratio of 60/3.5 = 17.
Moreover, to provide the initial pull necessary to wind the first few turns of the web on the core means that the starting rate of rotation of the shaft must be about 10% greater than what would be required when only surface speed and diameter are taken into consideration. In the typical example given here, the initial drive speed of the shaft would be approximately 1200 RPM. When the roll reaches its full 60 inch diameter the speed of rotation to maintain the stated web tension will go down from 1200 RPM to only about 64 RPM.
If A is the core diameter, B is the full roll diameter, S the surface speed of the web material and P is the web tension, the following formulas show the power requirements in the example stated above. (Conversion factors are included to give the results in horsepower).
The power to pull the material is: ##EQU1##
The power absorbed by the slip clutch, including 10% initial slip (maximum), is: ##EQU2##
The maximum total power required for winding is: ##EQU3##
Comparison of these power requirements will clearly show the great amount of power wasted when a slip clutch alone is employed to produce the required reduction in speed.
Considering the high speeds, and the large size of the rolls handled in modern paper, film and foil processing, the amount of wasted power caused by inefficient roll drive systems is extremely great.